Method for determining low-noise power spectral density for characterizing line edge roughness in semiconductor wafer processing

ABSTRACT

According to one exemplary embodiment, a method for determining a power spectral density of an edge of at least one patterned feature situated over a semiconductor wafer includes measuring the edge of the at least one patterned feature at a number of points on the edge. The method further includes determining an autoregressive estimation of the edge of the at least one patterned feature using measured data corresponding to a number of points on the edge. The method further includes determining a power spectral density of the edge using autoregressive coefficients from the autoregressive estimation. The method further includes utilizing the power spectral density to characterize line edge roughness of the at least one patterned feature in a frequency domain.

1. TECHNICAL FIELD

The present invention is generally in the field of electronics. Moreparticularly, the invention is in the field of semiconductor waferfabrication.

2. BACKGROUND ART

As semiconductor devices provided by modern semiconductor technologycontinue to scale down in size, critical dimension variation across asemiconductor wafer can significantly affect the production yield andelectrical performance of the devices fabricated on the wafer. A highpercentage of the critical dimension variation is caused by “line edgeroughness” resulting from lithographic processing of the semiconductorwafer. “Line edge roughness” refers to variations that occur along anedge of a patterned feature as a result of semiconductor waferprocessing. To understand the specific causes of line edge roughness,power spectral density for an edge of a patterned feature, such as atransistor gate, can be determined and utilized to analyze thedistribution of line edge roughness in the “frequency domain.”

In the present application, “frequency domain” refers to the summationof frequencies into which line edge roughness can be resolved. Line edgeroughness is typically measured in a spatial dimension, such as lengthof deviation from a reference line. However, the variations that occuralong the length of an edge of a patterned feature, i.e. the line edgeroughness, can be represented as a summation of different frequencycomponents, i.e., the “frequency domain” of the line edge roughness.

In a conventional approach, line edge roughness can be represented inthe frequency domain by determining power spectral density for an edgeof a patterned feature by utilizing a fast Fourier transform algorithm.In the conventional approach, line edge roughness is typically measuredby using a tool such as a scanning electron microscope. However, sincethe scanning electron microscope has limited sampling length andresolution, the power spectral density determined by the fast Fouriertransform algorithm includes a large amount of noise, which undesirablyreduces the accuracy of the line edge roughness represented by the powerspectral density.

SUMMARY

A method for determining low-noise power spectral density forcharacterizing line edge roughness in semiconductor wafer processing,substantially as shown in and/or described in connection with at leastone of the figures, and as set forth more completely in the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a top view of exemplary patterned features situatedover a portion of a semiconductor wafer.

FIG. 2 shows a flowchart illustrating typical steps taken to implementan embodiment of the present invention.

FIG. 3 is a graph showing an exemplary conventional power spectraldensity curve based on a fast Fourier transform.

FIG. 4 is a graph showing an exemplary power spectral density curve inaccordance with one embodiment of the present invention.

FIG. 5 illustrates a diagram of an exemplary electronic system includingan exemplary IC chip or semiconductor die fabricated by utilizing amethod of determining power spectral density of an edge of at least onepatterned feature in accordance with one embodiment of the presentinvention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention is directed to a method for determining low-noisepower spectral density for characterizing line edge roughness insemiconductor wafer processing. The following description containsspecific information pertaining to the implementation of the presentinvention. One skilled in the art will recognize that the presentinvention may be implemented in a manner different from thatspecifically discussed in the present application. Moreover, some of thespecific details of the invention are not discussed in order not toobscure the invention.

The drawings in the present application and their accompanying detaileddescription are directed to merely exemplary embodiments of theinvention. To maintain brevity, other embodiments of the presentinvention are not specifically described in the present application andare not specifically illustrated by the present drawings.

The present invention provides an innovative method of determiningaccurate, low-noise power spectral density of a line edge forcharacterizing line edge roughness of a patterned feature, such as atransistor gate, in the frequency domain. Although a line edge of apatterned feature comprising a resist material is utilized to illustratethe present invention, the present invention can generally be utilizedin semiconductor wafer processing to advantageously determine anaccurate, low-noise power spectral density of a line edge of a featurepatterned in any type of material, such as a conductive or dielectricmaterial.

FIG. 1 shows a top view of structure 100, which includes exemplaryfeatures situated over a layer. Structure 100 includes patternedfeatures 102, 104, and 106 and layer 108, which is situated over asubstrate (not shown in FIG. 1). Structure 100 can be a portion of asemiconductor wafer at an intermediate stage of fabrication. As shown inFIG. 1, patterned features 102, 104, and 106 are situated over layer 108and can comprise photoresist or other suitable resist material. Forexample, patterned features 102, 104, and 106 can be formed bydepositing a layer of photoresist over layer 108 and patterning thelayer of photoresist in a lithographic process. Patterned features 102,104, and 106 can each be utilized to pattern, for example, a gate of afield effect transistor (FET) in layer 108 in a subsequent etch process.

Also shown in FIG. 1, patterned feature 102 includes edge 110, which isalso referred to as a “line edge” in the present application, and haslength 114 and width 116, which can define, for example, correspondingdimensions of a subsequently patterned gate of a FET. For example, width116 can define gate length of a FET, which can be patterned in layer 108in a subsequent etch process. As a result of lithographic processing,variations occur along line edges of each of patterned features 102,104, and 106. The variations that occur along the line edges, such asedge 110 of patterned feature 102, can be referred to as “line edgeroughness.” For example, line edge roughness that occurs along edge 110of feature 102 is shown in expanded view 118 in FIG. 1.

Line edge roughness in features patterned in photoresist, such aspatterned features 102, 104, and 106, can be transferred tocorresponding device features, such as transistor gates, patterned inlayer 108 in a subsequent etch process. As a result, line edge roughnessalong edge 110 of feature 102 can cause line edge roughness along acorresponding gate edge. Line edge roughness that occurs along a gateedge can cause undesirable variations in gate length, which cansignificantly-affect device performance. Thus, line edge roughness cancause critical dimension variation across the wafer, which cansignificantly affect electrical performance of devices, such as FETs,fabricated on the wafer. Thus, it is important to understand the causesof line edge roughness so as to it (i.e. line edge roughness).

The present invention provides a method of determining low-noise powerspectral density for a line edge, such as edge 110, of a patternedfeature, such as patterned feature 102, so as to accurately characterizeline edge roughness of the patterned feature in the frequency domain.The invention's method for determining low-noise power spectral densityfor a line edge will be discussed below in relation to FIG. 2.

FIG. 2 shows a flowchart illustrating a method for determining low-noisepower spectral density of a line edge so as to accurately represent lineedge roughness in the frequency domain, in accordance with oneembodiment of the present invention. Certain details and features havebeen left out of flowchart 200 that are apparent to a person of ordinaryskill in the art. For example, a step may consist of one or moresubsteps or may involve specialized equipment or materials, as known inthe art. While steps 202, 204, 206, and 208 indicated in flowchart 200are sufficient to describe one embodiment of the present invention,other embodiments of the invention may utilize steps different fromthose shown in flowchart 200. It is noted that the steps shown inflowchart 200 are performed on a portion of a semiconductor wafer,which, prior to step 202, includes, among other things, a substrate andone or more overlying layers, such as dielectric and/or conductivelayers. The semiconductor wafer is also referred to simply as a wafer ora semiconductor die or simply a die in the present application. In oneembodiment, the steps shown in flowchart 200 can be performed on asemiconductor die, such as a microprocessor die, that is situated on thesemiconductor wafer.

Referring now to step 202 in FIG. 2, at step 202 of flowchart 200,patterned feature 102 in FIG. 1 is formed over layer 108, which issituated over a semiconductor wafer. For example, patterned feature 102can comprise photoresist and can be formed in a lithographic process.Patterned feature 102 can be utilized to form, for example, a transistorgate in layer 108 in a subsequent processing step. At step 204 offlowchart 200, edge 110 of patterned feature 102 is measured at aselected number of points. For example, edge 110 can be measured at eachof the selected number of points situated along edge 110 by utilizing atool such as a scanning electron microscope or an atomic forcemicroscope to acquiring an image of edge 110 including the selectedpoints and determining the coordinates of each point from the acquireimage. By measuring edge 110 of patterned feature 102 at each of theselected points, the line edge roughness at each of the selected pointsis also being measured.

At step 206 of flowchart 200, an autoregressive estimation of edge 110of patterned feature 102 is determined utilizing measured datacorresponding to the selected points. The measured data can include avalue for each selected point that corresponds to the coordinates ofthat point along the line edge. The autoregressive estimation of edge110 can be determined, for example, by utilizing the equation:

$\begin{matrix}{{z(k)} = {{n(k)} + {\sum\limits_{i = 1}^{N}\; {a_{i}{z\left( {k - i} \right)}}}}} & {{equation}\mspace{14mu} (1)}\end{matrix}$

where z(k) is an estimated value of edge 110 at point k, n(k) is a whitenoise sequence, a_(i) are autoregressive coefficients, and N is theautoregressive order. The autoregressive coefficients in equation (1)can be determined by using an autoregressive algorithm, such as theYule-Walker algorithm or the Burg algorithm. However, the autoregressivecoefficients can also be determined by using a covariance method, arecursive maximum likelihood estimation method, or other methods asknown by one of ordinary skill in the art.

A value for N, i.e., the autoregressive order in equation (1), can bedetermined, for example, by initially setting N=1, determining theautoregressive coefficients as discussed above, and determining z(k),i.e., an estimated value of edge 110 at point k. The difference betweenthe estimated value of z(k) from equation (1) and the measured value ofedge 110 at point k (as measured at step 204 of flowchart 200) is thendetermined. The above process is continued for N=2, N=3, etc. The valueof N is selected to be the value that results in the smallest differencebetween the estimated value of z(k) from equation (1) and the measuredvalue of edge 110 at point k. The value for N can also be determined byusing other methods as known in the art.

At step 208 of flowchart 200, the power spectral density of edge 110 ofpatterned feature 102 is determined by utilizing the autoregressivecoefficients, i.e., a_(i), and the autoregressive order determined fromthe autoregressive estimation of edge 110. After the autoregressivecoefficients and the autoregressive order have been the determined,power spectral density of edge 110 can be determined, for example, byutilizing the equation:

$\begin{matrix}{{S(f)} = \frac{ɛ^{2}\Delta \; z}{{1 + {\sum\limits_{i = 1}^{N}\; {a_{i}^{{- j}\; 2\pi \; \; f\; \Delta \; z}}}}}} & {{equation}\mspace{14mu} (2)}\end{matrix}$

where ε is a white noise sequence corresponding to the white noisespectrum power, f is frequency, a_(i) are the autoregressivecoefficients, N is the autoregressive order, and Δz is the resolution ofthe tool, such as a scanning electron microscope or an atomic forcemicroscope, that was utilized to measure edge 110 of patterned feature102 at step 204 of flowchart 200.

The power spectral density of edge 110 can be determined for a desiredrange of frequencies by plotting S(f) over the desired range offrequencies. The power spectral density, as determined by equation (2),is substantially noise-free and, thereby, provides an accuratecharacterization of line edge roughness of edge 110 of patterned feature102 in the frequency domain. The invention's power spectral density canbe utilized to quickly and accurately measure the relative intensity ofone or more of the component frequencies that determine the line edgeroughness of a line edge of a patterned feature.

The invention's power spectral density can be utilized to determine ifline edge roughness of patterned feature 102 meets predeterminedcriteria so as to monitor and improve semiconductor fabricationprocesses, such as lithographic processes. For example, if the line edgeroughness of edge 110 of patterned feature 102 meets the predeterminedcriteria, which can be determined from previous measurement data, waferprocessing can continue by patterning a gate of a FET corresponding topatterned feature 102 in an underlying layer situated over the wafer.For example, if the line edge roughness of edge 110 of patterned feature102 does not meet the predetermined criteria, patterned feature 102 canbe removed from the wafer and it can be can be re-formed with newphotoresist.

By utilizing the present invention, an overall power spectral densitycan be determined across a wafer by quickly and accurately determinepower spectral densities for a few line edges on the wafer. The overallpower spectral density can be advantageously utilized to predict CD(critical dimension) variation across the wafer, such as gate lengthvariation across the wafer. By predicting CD variation across the wafer,related electrical characteristics of devices, such as FETs, can also bepredicted.

FIG. 3 shows graph 300 including exemplary power spectral densitycurves. Graph 300 includes power spectral density axis 302, spatialfrequency axis 304, ideal power spectral density curve 306, andconventional power spectral density curve 308. In graph 300, powerspectral density axis 302 shows an exemplary range of normalized powerspectral density and spatial frequency axis 304 shows an exemplary rangeof spatial frequencies. Power spectral density is normalized on powerspectral density axis 302 and, therefore, has no units. On spatialfrequency axis 304, “spatial frequency” refers to the inverse of aperiod, i.e., one over the period, of a frequency component of line edgeroughness. As discussed above, line edge roughness can be resolved intoa summation of different frequency components, i.e., the “frequencydomain” of the line edge roughness. Thus, spatial frequency axis 304shows the inverse of a range of periods of the frequency components thatform the line edge roughness.

In graph 300, ideal power spectral density curve 306 (shown as a solidline in graph 300) is an ideal power spectral density curve used togenerate the line edge (corresponding to a known line edge). Also ingraph 300, conventional power spectral density curve 308 (shown as aseries of vertical broken lines in graph 300) corresponds to a powerspectral density curve that is generated by utilizing a fast Fouriertransform algorithm for the line edge generated with curve 306.

In the example shown in graph 300, conventional power spectral densitycurve 308 includes a large amount of noise, which is indicated in graph300 by vertical broken lines that extend above and below ideal powerspectral density curve 306. The large amount of noise in conventionalpower spectral density curve 308 occurs as a result of the fast Fouriertransform algorithm utilized to generate the curve. As a result of thelarge amount of noise in conventional power spectral density curve 308,it (i.e. conventional power spectral density curve 308) inaccuratelycharacterizes line edge roughness by inaccurately representing thefrequency components of line edge roughness.

FIG. 4 shows graph 400 including autoregressive-based power spectraldensity curve 408 in accordance with one embodiment of the presentinvention. Graph 400 includes power spectral density axis 402, spatialfrequency axis 404, ideal power spectral density curve 406, andautoregressive-based power spectral density curve 408. In graph 400,power spectral density axis 402 shows an exemplary range of normalizedpower spectral density and spatial frequency axis 404 shows an exemplaryrange of spatial frequencies.

In graph 400, ideal power spectral density curve 406 (shown as a solidline in graph 400) corresponds to ideal power spectral density curve 306in graph 300 in FIG. 3. Also in graph 400, autoregressive-based powerspectral density curve 408 corresponds to a power spectral density curvethat is generated by utilizing an autoregressive technique, whichincludes determining an autoregressive estimation of a line edge asdiscussed in flowchart 200 in FIG. 2.

In the example shown in graph 400, autoregressive-based power spectraldensity curve 408 has substantially no noise and accurately tracks idealpower spectral density curve 408. As a result, autoregressive-basedpower spectral density curve 408 accurately represents the frequencycomponents of line edge roughness of a line edge. Thus, in contrast toconventional power spectral density curve 308 in FIG. 3, which isgenerated utilizing a fast Fourier transform algorithm,autoregressive-based power spectral density curve 408, which isgenerated according to an embodiment of the present invention, canaccurately characterize line edge roughness of a line edge in thefrequency domain.

FIG. 5 illustrates a diagram of an exemplary electronic system includingan exemplary chip or die fabricated by utilizing a power spectraldensity of an edge of at least one patterned featured determined inaccordance with one embodiment of the present invention. Electronicsystem 500 includes exemplary modules 502, 504, and 506, IC chip 508(also referred to as semiconductor die 508 in the present application),discrete components 510 and 512, residing in and interconnected throughcircuit board 514. In one embodiment, electronic system 500 may includemore than one circuit board. IC chip 508 can comprise a semiconductordie that is fabricated by using an embodiment of the invention's methodfor determining power spectral density of an edge of at least onepatterned feature, such as the method of flowchart 200 in FIG. 2. Forexample, the power spectral density can be utilized to characterize lineedge roughness of the patterned feature in the frequency domain in alithographic process during fabrication of the semiconductor die. ICchip 508 includes circuit 516, which can be a microprocessor, forexample.

As shown in FIG. 5, modules 502, 504, and 506 are mounted on circuitboard 514 and can each be, for example, a central processing unit (CPU),a graphics controller, a digital signal processor (DSP), an applicationspecific integrated circuit (ASIC), a video processing module, an audioprocessing module, an RF receiver, an RF transmitter, an image sensormodule, a power control module, an electro-mechanical motor controlmodule, or a field programmable gate array (FPGA), or any other kind ofmodule utilized in modern electronic circuit boards. Circuit board 514can include a number of interconnect traces (not shown in FIG. 5) forinterconnecting modules 502, 504, and 506, discrete components 510 and512, and IC chip 508.

Also shown in FIG. 5, IC chip 508 is mounted on circuit board 514 andcan comprise, for example, any semiconductor die that is fabricated byutilizing an embodiment of the invention's method for determining powerspectral density of an edge of at least one patterned feature. In oneembodiment, IC chip 508 may not be mounted on circuit board 514, and maybe interconnected with other modules on different circuit boards.Further shown in FIG. 5, discrete components 510 and 512 are mounted oncircuit board 514 and can each be, for example, a discrete filter, suchas one including a BAW or SAW filter or the like, a power amplifier oran operational amplifier, a semiconductor device, such as a transistoror a diode or the like, an antenna element, an inductor, a capacitor, ora resistor.

Electronic system 500 can be utilized in, for example, a wiredcommunications device, a wireless communications device, a cell phone, aswitching device, a router, a repeater, a codec, a LAN, a WLAN, aBluetooth enabled device, a digital camera, a digital audio playerand/or recorder, a digital video player and/or recorder, a computer, amonitor, a television set, a satellite set top box, a cable modem, adigital automotive control system, a digitally-controlled homeappliance, a printer, a copier, a digital audio or video receiver, an RFtransceiver, a personal digital assistant (PDA), a digital game playingdevice, a digital testing and/or measuring device, a digital avionicsdevice, a medical device, or a digitally-controlled medical equipment,or in any other kind of system, device, component or module utilized inmodern electronics applications.

As discussed above, the invention provides a method for determininglow-noise power spectral density for one or more line edges of patternedfeatures formed over a semiconductor wafer. By determining low-noisepower spectral density for a line edge, the invention advantageouslyallows line edge roughness to be quickly and accurately characterizedfor a patterned feature in the frequency domain.

From the above description of the invention it is manifest that varioustechniques can be used for implementing the concepts of the presentinvention without departing from its scope. Moreover, while theinvention has been described with specific reference to certainembodiments, a person of ordinary skill in the art would appreciate thatchanges can be made in form and detail without departing from the spiritand the scope of the invention. Thus, the described embodiments are tobe considered in all respects as illustrative and not restrictive. Itshould also be understood that the invention is not limited to theparticular embodiments described herein but is capable of manyrearrangements, modifications, and substitutions without departing fromthe scope of the invention.

Thus, a method for determining low-noise power spectral density forcharactering line edge roughness in semiconductor wafer processing hasbeen described.

1. A method for determining a power spectral density of an edge of atleast one patterned feature situated over a semiconductor wafer, saidmethod comprising steps of: determining an autoregressive estimation ofsaid edge of said at least one patterned feature using measured datacorresponding to a plurality of points on said edge; determining a powerspectral density of said edge using autoregressive coefficients fromsaid autoregressive estimation.
 2. The method of claim 1 furthercomprising utilizing said power spectral density to characterize lineedge roughness of said at least one patterned feature in a frequencydomain.
 3. The method of claim 1 further comprising utilizing saidmethod of determining said power spectral density of said edge of saidat least one patterned feature to fabricate a semiconductor die.
 4. Themethod of claim 3 further comprising utilizing said semiconductor die ina circuit board.
 5. The method of claim 1 further comprising a step ofmeasuring said edge of said at least one patterned feature at saidplurality of points situated on said edge prior to said step ofdetermining said autoregressive estimation.
 6. The method of claim 1,wherein said autoregressive coefficients are determined by using anautoregressive algorithm.
 7. The method of claim 6, wherein saidautoregressive algorithm is selected from the group consisting of a Borgalgorithm and a Yule-Walker algorithm.
 8. The method of claim 1, whereinsaid at least one patterned feature is utilized to patterned atransistor gate in an underlying layer.
 9. The method of claim 1,wherein said step of determining said autoregressive estimation of saidedge includes determining an autoregressive order for saidautoregressive estimation.
 10. The method of claim 1, wherein saidautoregressive estimation of said edge is determined by:${{z(k)} = {{n(k)} + {\sum\limits_{i = 1}^{N}\; {a_{i}{z\left( {k - i} \right)}}}}};$wherein z(k) is an estimated value of said edge at one of said pluralityof points, n(k) is a white noise sequence, a_(i) are said autoregressivecoefficients, and N is an autoregressive order.
 11. The method of claim1, wherein said power spectral density is determined by:${{S(f)} = \frac{ɛ^{2}\Delta \; z}{{1 + {\sum\limits_{i = 1}^{N}\; {a_{i}^{{- j}\; 2{\pi }\; f\; \Delta \; z}}}}}};$wherein ε is a white noise sequence, f is a frequency, a_(i) are saidautoregressive coefficients, N is an autoregressive order, and Δz is aresolution of a tool utilized to measure said edge of said patternedfeature.
 12. A semiconductor die fabricated by utilizing a method fordetermining a power spectral density of an edge of at least onepatterned feature, said method comprising steps of: forming said atleast one patterned feature over a substrate of said semiconductor die;determining an autoregressive estimation of said edge of said at leastone patterned feature using measured data corresponding to a pluralityof points on said edge; determining a power spectral density of saidedge using autoregressive coefficients from said autoregressiveestimation.
 13. The semiconductor die of claim 12, wherein said methodfurther comprises utilizing said power spectral density to characterizeline edge roughness of said at least one patterned feature in afrequency domain.
 14. The semiconductor die of claim 12, wherein saidmethod further comprises a step of measuring said edge of said at leastone patterned feature at said plurality of points situated on said edgeprior to said step of determining said autoregressive estimation. 15.The semiconductor die of claim 12, wherein said autoregressivecoefficients are determined by using an autoregressive algorithm. 16.The semiconductor die of claim 14, wherein said step of measuring saidedge of said at least one patterned feature comprises utilizing a toolselected from the group consisting of a scanning electron microscope andan atomic force microscope.
 17. The semiconductor die of claim 12,wherein said at least one patterned feature comprises photoresist. 18.The semiconductor die of claim 12, wherein said at least one patternedfeature is utilized to patterned a transistor gate in an underlyinglayer.
 19. The semiconductor die of claim 12, wherein saidautoregressive estimation of said edge is determined by:${{z(k)} = {{n(k)} + {\sum\limits_{i = 1}^{N}\; {a_{i}{z\left( {k - i} \right)}}}}};$wherein z(k) is an estimated value of said edge at one of said pluralityof points, n(k) is a white noise sequence, a_(i) are said autoregressivecoefficients, and N is an autoregressive order.
 20. The semiconductordie of claim 12, wherein said power spectral density is determined by:${{S(f)} = \frac{ɛ^{2}\Delta \; z}{{1 + {\sum\limits_{i = 1}^{N}\; {a_{i}^{{- j}\; 2\pi \; \; f\; \Delta \; z}}}}}};$wherein ε is a white noise sequence, f is a frequency, a_(i) are saidautoregressive coefficients, N is an autoregressive order, and Δz is aresolution of a tool utilized to measure said edge of said patternedfeature.